YEAR 8 MATHS FOCUS
NUMBER AND ALGEBRA
Financial Mathematics
Learning Experiences
Concept Teaching
Financial Mathematics
FINANCIAL MATHEMATICS
OUTCOME
A student:
MA4-6NA:
solves financial problems involving purchasing goods
| TEACHING POINTS | The Goods and Services Tax (GST) in Australia is a value-added tax on the supply of goods and services. It was introduced by the Australian Government and took effect from 1 July 2000. Prior to the GST, Australia operated a wholesale sales tax implemented in the 1930s, when its economy was dominated by the production and sale of goods. In Australia, the GST is levied at a flat rate of 10% on most goods and services, apart from GST-exempt items (which include basic necessities such as milk and bread). |
| LANGUAGE | GST stands for ‘Goods and Services Tax’. The difference between the GST-inclusive price, the pre-GST price, and the amount of the GST itself should be made explicit. When solving financial problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working, and to conclude with a statement in words. Students’ understanding may be increased if they write calculations in words first, before substituting the appropriate values, e.g. percentage discount=discount/retail price×100% Students may need assistance with the subtleties of language used in relation to financial transactions, e.g. the difference between ‘$100 has been discounted by $10’ and ‘$100 has been discounted to $10’. |
| PURPOSE RELEVANCE | Financial mathematics’ is used in important areas relating to an individual’s daily financial transactions, money management, and financial decision making. Such areas include earning and spending money (eg calculating ‘best buys’, discounts, GST, personal taxation, profit and loss, investing money, credit and borrowing, hire purchase, simple and compound interest, loan repayments, and depreciation. |
Expectations of Attainment
Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123) | select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbers |
| select and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a one-digit divisor, including where there is a remainder | |
| – estimate solutions to problems and check to justify solutions {Problem Solving, Reasoning, Critical and creative thinking} | |
| use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiples | |
| solve word problems involving multiplication and division, e.g. ‘A recipe requires 3 cups of flour for 10 people. How many cups of flour are required for 40 people?’ {Critical and creative thinking} | |
| – use appropriate language to compare quantities, e.g. ‘twice as much as’, ‘half as much as’ {Communicating, Critical and creative thinking} | |
| – use a table or similar organiser to record methods used to solve problems {Communicating, Problem Solving, Information and communication technology capability} | |
| recognise symbols used to record speed in kilometres per hour, e.g. 80 km/h {Literacy} | |
| solve simple problems involving speed, e.g. ‘How long would it take to travel 600 km if the average speed for the trip is 75 km/h?’ {Critical and creative thinking} |
Explore the use of brackets and the order of operations to write number sentences (ACMNA134) | use the term ‘operations’ to describe collectively the processes of addition, subtraction, multiplication and division |
| investigate and establish the order of operations using real-life contexts, e.g. ‘I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?’; this can be represented by the number sentence 6 × 10 + 2 × 4 but, to obtain the total cost, multiplication must be performed before addition {Literacy, Critical and creative thinking, Work and enterprise} | |
| – write number sentences to represent real-life situations {Communicating, Problem Solving, Literacy} | |
| recognise that the grouping symbols ( ) and [ ] are used in number sentences to indicate operations that must be performed first {Literacy} | |
| recognise that if more than one pair of grouping symbols are used, the operation within the innermost grouping symbols is performed first | |
perform calculations involving grouping symbols without the use of digital technologies, (2+3)×(16−9)=5×7 3+[20÷(9−5)]=3+[20÷4]=3+5 | |
apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies, e.g. 32÷2×4=16×4 32÷(2×4)=32÷8 (32+2)×4=34×4 32+2×4=32+8 {Work and enterprise} | |
| – investigate whether different digital technologies apply the order of operations {Reasoning, Information and communication technology capability, Critical and creative thinking} | |
| recognise when grouping symbols are not necessary, eg 32 + (2 × 4) has the same answer as 32 + 2 × 4 |
Learning Experiences
To be added
Concept Teaching
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